1. The problem statement, all variables and given/known data
A solid cylinder is rolling without slipping. What fraction of its kinetic energy is linear?
2. Relevant equations
Ke=[itex]\frac{mv^2}{2}[/itex]+[itex]\frac{I(v/r)^2}{2}[/itex]
3. The attempt at a solution
Ke=[itex]\frac{mv^2}{2}[/itex]+[itex]\frac{(v/r)^2}{2}[/itex]*[itex]\frac{(mr)^2}{2}[/itex]
Ke=[itex]\frac{3(mv)^2}{4}[/itex]
Linear Ke =[itex]\frac{(mv)^2}{4}[/itex]
Fraction of Linear Ke = [itex]\frac{linear Ke}{Ke}[/itex] = [itex]\frac{(1/4)}{(3/4)}[/itex] = [itex]\frac{1}{3}[/itex]
A solid cylinder is rolling without slipping. What fraction of its kinetic energy is linear?
2. Relevant equations
Ke=[itex]\frac{mv^2}{2}[/itex]+[itex]\frac{I(v/r)^2}{2}[/itex]
3. The attempt at a solution
Ke=[itex]\frac{mv^2}{2}[/itex]+[itex]\frac{(v/r)^2}{2}[/itex]*[itex]\frac{(mr)^2}{2}[/itex]
Ke=[itex]\frac{3(mv)^2}{4}[/itex]
Linear Ke =[itex]\frac{(mv)^2}{4}[/itex]
Fraction of Linear Ke = [itex]\frac{linear Ke}{Ke}[/itex] = [itex]\frac{(1/4)}{(3/4)}[/itex] = [itex]\frac{1}{3}[/itex]
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